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Автор: Grafiati
Опубліковано: 10 грудня 2022
Оновлено: 28 січня 2023

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Статті в журналах з теми "010501 Algebraic Structures in Mathematical Physics"

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Freed, Daniel S. "Higher algebraic structures and quantization." Communications in Mathematical Physics 159, no. 2 (January 1994): 343–98. http://dx.doi.org/10.1007/bf02102643.

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2

Gangopadhyay, Sunandan. "Lie algebraic noncommuting structures from reparametrization symmetry." Journal of Mathematical Physics 48, no. 5 (May 2007): 052302. http://dx.doi.org/10.1063/1.2723551.

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3

Duplij, Steven. "Arity Shape of Polyadic Algebraic Structures." Zurnal matematiceskoj fiziki, analiza, geometrii 15, no. 1 (March 25, 2019): 3–56. http://dx.doi.org/10.15407/mag15.01.003.

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4

Kulish, P. P., and E. K. Sklyanin. "Algebraic structures related to reflection equations." Journal of Physics A: Mathematical and General 25, no. 22 (November 21, 1992): 5963–75. http://dx.doi.org/10.1088/0305-4470/25/22/022.

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5

Kramer, P. "Algebraic structures for 1D quasiperiodic systems." Journal of Physics A: Mathematical and General 26, no. 2 (January 21, 1993): 213–28. http://dx.doi.org/10.1088/0305-4470/26/2/010.

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6

Hammad, M. M., H. E. Shetawy, Ayman A. Aly, and S. B. Doma. "Nuclear supersymmetry and dual algebraic structures." Physica Scripta 94, no. 10 (August 6, 2019): 105207. http://dx.doi.org/10.1088/1402-4896/ab2442.

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Rajchel-Mieldzioć, Grzegorz, Kamil Korzekwa, Zbigniew Puchała, and Karol Życzkowski. "Algebraic and geometric structures inside the Birkhoff polytope." Journal of Mathematical Physics 63, no. 1 (January 1, 2022): 012202. http://dx.doi.org/10.1063/5.0046581.

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8

Cardoso, Pedro G. S., Ernesto P. Borges, Thierry C. P. Lobão, and Suani T. R. Pinho. "Nondistributive algebraic structures derived from nonextensive statistical mechanics." Journal of Mathematical Physics 49, no. 9 (September 2008): 093509. http://dx.doi.org/10.1063/1.2982233.

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9

Harrelson, Eric, Alexander A. Voronov, and J. Javier Zúñiga. "Open-Closed Moduli Spaces and Related Algebraic Structures." Letters in Mathematical Physics 94, no. 1 (September 1, 2010): 1–26. http://dx.doi.org/10.1007/s11005-010-0418-0.

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10

KERNER, RICHARD. "TERNARY AND NON-ASSOCIATIVE STRUCTURES." International Journal of Geometric Methods in Modern Physics 05, no. 08 (December 2008): 1265–94. http://dx.doi.org/10.1142/s0219887808003326.

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Анотація:
We discuss ternary algebraic structures appearing in various domains of theoretical and mathematical physics. Some of them are associative, and some are not. Their interesting and curious properties can be exploited in future applications to enlarged and generalized field theoretical models in the years to come. Many ideas presented here have been developed and clarified in countless discussions with Michel Dubois-Violette.
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Дисертації з теми "010501 Algebraic Structures in Mathematical Physics"

1

(9143375), Kang Lu. "Gaudin models associated to classical Lie algebras." Thesis, 2020.

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Анотація:
We study the Gaudin model associated to Lie algebras of classical types.

First, we derive explicit formulas for solutions of the Bethe ansatz equations of the Gaudin model associated to the tensor product of one arbitrary finite-dimensional irreducible module and one vector representation for all simple Lie algebras of classical type. We use this result to show that the Bethe Ansatz is complete in any tensor product where all but one factor are vector representations and the evaluation parameters are generic. We also show that except for the type D, the joint spectrum of Gaudin Hamiltonians in such tensor products is simple.

Second, we define a new stratification of the Grassmannian of N planes. We introduce a new subvariety of Grassmannian, called self-dual Grassmannian, using the connections between self-dual spaces and Gaudin model associated to Lie algebras of types B and C. Then we obtain a stratification of self-dual Grassmannian.
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2

(8766687), Luan Pereira Bezerra. "Quantum Toroidal Superalgebras." Thesis, 2020.

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Анотація:
We introduce the quantum toroidal superalgebra Em|n associated with the Lie superalgebra glm|n and initiate its study. For each choice of parity "s" of glm|n, a corresponding quantum toroidal superalgebra Es is defined.

To show that all such superalgebras are isomorphic, an action of the toroidal braid group is constructed.

The superalgebra Es contains two distinguished subalgebras, both isomorphic to the quantum affine superalgebra Uq sl̂m|n with parity "s", called vertical and horizontal subalgebras. We show the existence of Miki automorphism of Es, which exchanges the vertical and horizontal subalgebras.

If m and n are different and "s" is standard, we give a construction of level 1 Em|n-modules through vertex operators. We also construct an evaluation map from Em|n(q1,q2,q3) to the quantum affine algebra Uq gl̂m|n at level c=q3(m-n)/2.
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3

(9115211), Chenliang Huang. "ON THE GAUDIN AND XXX MODELS ASSOCIATED TO LIE SUPERALGEBRAS." Thesis, 2020.

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Анотація:
We describe a reproduction procedure which, given a solution of the gl(m|n) Gaudin Bethe ansatz equation associated to a tensor product of polynomial modules, produces a family P of other solutions called the population.
To a population we associate a rational pseudodifferential operator R and a superspace W of rational functions.

We show that if at least one module is typical then the population P is canonically identified with the set of minimal factorizations of R and with the space of full superflags in W. We conjecture that the singular eigenvectors (up to rescaling) of all gl(m|n) Gaudin Hamiltonians are in a bijective correspondence with certain superspaces of rational functions.

We establish a duality of the non-periodic Gaudin model associated with superalgebra gl(m|n) and the non-periodic Gaudin model associated with algebra gl(k).

The Hamiltonians of the Gaudin models are given by expansions of a Berezinian of an (m+n) by (m+n) matrix in the case of gl(m|n)
and of a column determinant of a k by k matrix in the case of gl(k). We obtain our results by proving Capelli type identities for both cases and comparing the results.

We study solutions of the Bethe ansatz equations of the non-homogeneous periodic XXX model associated to super Yangian Y(gl(m|n)).
To a solution we associate a rational difference operator D and a superspace of rational functions W. We show that the set of complete factorizations of D is in canonical bijection with the variety of superflags in W and that each generic superflag defines a solution of the Bethe ansatz equation. We also give the analogous statements for the quasi-periodic supersymmetric spin chains.
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4

(9121400), Filipp Uvarov. "Duality of Gaudin Models." Thesis, 2020.

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Анотація:
We consider actions of the current Lie algebras $\gl_{n}[t]$ and $\gl_{k}[t]$ on the space $\mathfrak{P}_{kn}$ of polynomials in $kn$ anticommuting variables. The actions depend on parameters $\bar{z}=(z_{1}\lc z_{k})$ and $\bar{\alpha}=(\alpha_{1}\lc\alpha_{n})$, respectively.
We show that the images of the Bethe algebras $\mathcal{B}_{\bar{\alpha}}^{\langle n \rangle}\subset U(\gl_{n}[t])$ and $\mathcal{B}_{\bar{z}}^{\langle k \rangle}\subset U(\gl_{k}[t])$ under these actions coincide.
To prove the statement, we use the Bethe ansatz description of eigenvectors of the Bethe algebras via spaces of quasi-exponentials. We establish an explicit correspondence between the spaces of quasi-exponentials describing eigenvectors of $\mathcal{B}_{\bar{\alpha}}^{\langle n \rangle}$ and the spaces of quasi-exponentials describing eigenvectors of $\mathcal{B}_{\bar{z}}^{\langle k \rangle}$.
One particular aspect of the duality of the Bethe algebras is that the Gaudin Hamiltonians exchange with the Dynamical Hamiltonians. We study a similar relation between the trigonometric Gaudin and Dynamical Hamiltonians. In trigonometric Gaudin model, spaces of quasi-exponentials are replaced by spaces of quasi-polynomials. We establish an explicit correspondence between the spaces of quasi-polynomials describing eigenvectors of the trigonometric Gaudin Hamiltonians and the spaces of quasi-exponentials describing eigenvectors of the trigonometric Dynamical Hamiltonians.
We also establish the $(\gl_{k},\gl_{n})$-duality for the rational, trigonometric and difference versions of Knizhnik-Zamolodchikov and Dynamical equations.
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Книги з теми "010501 Algebraic Structures in Mathematical Physics"

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Seminar on Deformations (1988-1992 Łódź, Poland and Malinka, Poland). Deformations of mathematical structures II: Hurwitz-type structures and applications to surface physics : selected papers from the Seminar on Deformations, Łódź-Malinka,1988/92. Dordrecht: Kluwer Academic Publishers, 1994.

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2

International Colloquium on Group Theoretical Methods in Physics (18th 1990 Moscow, USSR). Symmetries and algebraic structures in physics: Proceedings of the XVIII International Colloquium on Group Theoretical Methods in Physics, Moscow, USSR, June 4-9, 1990. Commack, N.Y: Nova Science, 1991.

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3

International Workshop on Complex Structures, Integrability, and Vector Fields (10th 2010 Sofia, Bulgaria). International Workshop on Complex Structures, Integrability, and Vector Fields, Sofia, Bulgaria, 13-17 September 2010. Edited by Sekigawa Kouei. Melville, N.Y: American Institute of Physics, 2011.

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4

Representation theory and mathematical physics: Conference in honor of Gregg Zuckerman's 60th birthday, October 24--27, 2009, Yale University. Providence, R.I: American Mathematical Society, 2011.

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5

Misra, Kailash C., Milen Yakimov, Pramod N. Achar, and Dijana Jakelic. Recent advances in representation theory, quantum groups, algebraic geometry, and related topics: AMS special sessions on geometric and algebraic aspects of representation theory and quantum groups, and noncommutative algebraic geometry, October 13-14, 2012, Tulane University, New Orleans, Louisiana. Providence, Rhode Island: American Mathematical Society, 2014.

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6

Dzhamay, Anton, Ken'ichi Maruno, and Christopher M. Ormerod. Algebraic and analytic aspects of integrable systems and painleve equations: AMS special session on algebraic and analytic aspects of integrable systems and painleve equations : January 18, 2014, Baltimore, MD. Providence, Rhode Island: American Mathematical Society, 2015.

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7

Burgos Gil, José I. (José Ignacio), 1962- editor, ed. Feynman amplitudes, periods, and motives: International research conference on periods and motives : a modern perspective on renormalization : July 2-6, 2012, Institute de Ciencias Matematicas, Madris, Spain. Providence, Rhode Island: American Mathematical Society, 2015.

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8

editor, Donagi Ron, Katz Sheldon 1956 editor, Klemm Albrecht 1960 editor, and Morrison, David R., 1955- editor, eds. String-Math 2012: July 16-21, 2012, Universität Bonn, Bonn, Germany. Providence, Rhode Island: American Mathematical Society, 2015.

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9

1975-, Sims Robert, and Ueltschi Daniel 1969-, eds. Entropy and the quantum II: Arizona School of Analysis with Applications, March 15-19, 2010, University of Arizona. Providence, R.I: American Mathematical Society, 2011.

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10

Duplij, Steven. Exotic Algebraic and Geometric Structures in Theoretical Physics. Nova Science Publishers, Incorporated, 2018.

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Частини книг з теми "010501 Algebraic Structures in Mathematical Physics"

1

Thelen, S. "Algebraic spin structures." In Clifford Algebras and their Applications in Mathematical Physics, 143–49. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8090-8_15.

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2

Schenberg, Mario. "Algebraic Structures of Finite Point Sets I." In Clifford Algebras and their Applications in Mathematical Physics, 505–18. Dordrecht: Springer Netherlands, 1992. http://dx.doi.org/10.1007/978-94-015-8090-8_47.

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3

"Algebraic Structures." In Topics in Contemporary Mathematical Physics, 37–40. WORLD SCIENTIFIC, 2015. http://dx.doi.org/10.1142/9789814667814_0005.

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4

"Algebraic Structures." In Topics in Contemporary Mathematical Physics, 37–40. WORLD SCIENTIFIC, 2003. http://dx.doi.org/10.1142/9789812775443_0005.

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Тези доповідей конференцій з теми "010501 Algebraic Structures in Mathematical Physics"

1

Osborne, Alfred R. "Theory of Nonlinear Fourier Analysis: The Construction of Quasiperiodic Fourier Series for Nonlinear Wave Motion." In ASME 2020 39th International Conference on Ocean, Offshore and Arctic Engineering. American Society of Mechanical Engineers, 2020. http://dx.doi.org/10.1115/omae2020-18850.

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Анотація:
Abstract I give a description of nonlinear water wave dynamics using a recently discovered tool of mathematical physics I call nonlinear Fourier analysis (NLFA). This method is based upon and is an application of a theorem due to Baker [1897, 1907] and Mumford [1984] in the field of algebraic geometry and from additional sources by the author [Osborne, 2010, 2018, 2019]. The theory begins with the Kadomtsev-Petviashvili (KP) equation, a two dimensional generalization of the Korteweg-deVries (KdV) equation: Here the NLFA method is derived from the complete integrability of the equation by finite gap theory or the inverse scattering transform for periodic/quasiperiodic boundary conditions. I first show, for a one-dimensional, plane wave solution, that the KP equation can be rotated to a solution of the KdV equation, where the coefficients of KdV are now functions of the rotation angle. I then show how the rotated KdV equation can be used to compute the spectral solutions of the KP equation itself. Finally, I write the spectral solutions of the KP equation as a finite gap solution in terms of Riemann theta functions. By virtue of the fact that I am able to write a theta function formulation of the KP equation, it is clear that the wave dynamics lie on tori and constitute parallel dynamics on the tori in the integrable cases and non-parallel dynamics on the tori for certain perturbed quasi-integrable cases. Therefore, we are dealing with a Kolmogorov-Arnold-Moser KAM theory for nonlinear partial differential wave equations. The nonlinear Fourier series have particular nonlinear Fourier modes, including: sine waves, Stokes waves and solitons. Indeed the theoretical formulation I have developed is a kind of exact two-dimensional “coherent wave turbulence” or “integrable wave turbulence” for the KP equation, for which the Stokes waves and solitons are the coherent structures. I discuss how NLFA provides a number of new tools that apply to a wide range of problems in offshore engineering and coastal dynamics: This includes nonlinear Fourier space and time series analysis, nonlinear Fourier wave field analysis, a nonlinear random phase approximation, the study of nonlinear coherent functions and nonlinear bi and tri spectral analysis.
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